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0270~6474/82/0201-0032$02.00/O Copyright 0 Society for Neuroscience Printed in U.S.A. The Journal of Neuroscience Vol. 2, No. 1, pp. 32-48 January 1982 THEORY FOR THE DEVELOPMENT OF NEURON SEL EC TIVITY: ORIENTATION SPECIFICITY AND BINOCULAR INTERACTI ON IN VISUAL CORTEX1 ELIE L. BIENENSTOCK ,2 LEON N COOPER,3 AND PAUL W. MUNRO Center for Neural Science, Department of Phys ics, and Division of Appli ed Mathematics, Brown Univ ersi ty, Providence, Rhode Island 02912 Received June 5, 1981; Revised August 27, 1981; Accepted September 1, 1981 Abstract The development of sti mul us selectivity in the primary sensory corte x of higher vertebrates is considered in a general mathematical frame work. A sy naptic evolut ion scheme of a new kind i s proposed in which incoming patterns rather than converging afferents compete. The change in the effic acy of a given synapse depends not onl y on instantaneous pre- and postsynaptic activities but als o on a slowly varying time-averaged value of the postsynaptic acti vity . Assuming an appropriate nonlinear form for this dependence, development of selec tivity is obtained under quite general condi tions on the sensory environment. One does not require nonlinearity of the neuron’ s integrative power nor does one need to ass ume any particular form for intracortical circuitry. This is first alternately in a random manner. The following formal statement then holds : the state of the system converges with probability 1 to points of maximum selectivity in t he state space. We next cons ider the problem of early development of orientation selectivity and binocular interaction in primary visual cortex. Giving the environment an appropriate form, we obtain orient ation tuning curves and ocular dominance comparable to wh at is observed in normally reared adult cats or monkeys . Simulations with binocular input and various types of normal or al tered environm ents show good agreement with the relevant experimental data. Experiments are suggested that coul d test our theory further. It ha s been known for s ome time that sensory neurons at practi cally all levels display various fo rms of stimul us selectivity. They may respond preferentially to a tone of a given frequency, a light spot of a given color, a light bar of a certain length, retinal disparity, orientation, etc. We might, therefore, regard stimulus selectivity as a general property of sensory neurons and conjecture that the development of such selectivity obeys some general rule. Most attract ive is the idea that s ome of the mech- anisms by which selectivity develops in embryonic or early postnat al lif e are sufficiently general to allow a unifying theoretical treatment. ’ This work was supported in part by United States Office of Naval Research Contract NOOO14-81-K-0136, the Fondation de France, and the Ittleson Foundation, Inc. We would like to express our appreciation to our colleagues at the Brown University Center for Neural Science for their interest and helpful advice. In particular, we thank Professor Stuart Geman for several useful discu ssions. 2 Present address: Laboratoire de statistique appliquee, Batiment 425, Universite de Paris Sud, 91405 Orsay, France. ’ To whom correspondence should be addressed at Center for Neural Science, Brown Universi ty, Providence, RI 02912. In the present paper, we attempt to construct such a mathematical theory of the development of sti mul us selectivity in co rtex. It is based on (I ) an elementary definition of a general index of selectivity and (2) sto- chastic differential equations proposed as a description of the evolution of the strengths of all synaptic junctions onto a given cortical neuron. The ontogenetic development of the visual system, particularly of higher vertebrates, has been studi ed ve ry extensi vely. Since the work of Hubel and Wiesel (1959, 1962), it has been known that almost all neurons in the primary visual cortex (area 17) of the normally reared adult cat are selective; they respond in a preci se and sometimes highly tuned fashion to a variety of features- in parti cular, to bars or edges of a given orien tation and/ or those moving in a given direction through their recep- tive field s. Further work has shown that the response characteristics of these cortical cells strongly depend on the visual environment experienced by the animal during a critical period extending roughly from the 3rd to the 15th week of postnat al life (see, for example, Hubel and Wiesel, 1965; Blakemore and Van Sluyters, 1975; Buis-
